In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

in this paper, we study the convexity of the integral operator

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...

In this paper, we present some operator and eigenvalue inequalities involving monotone, doubly concave convex functions. These provide variants of Acz\'{e}l inequality its reverse via generalized Kantorovich constant.

In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore,  the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some  characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtai...

Let X,Y be normed spaces. The set of bounded linear operators is noted as L(X,Y ). Let now D = D(A) ⊂ X be a linear subspace, and A : D −→ Y a linear (not necessarily bounded!) operator. Notation: (A,D(A)) : X −→ Y Definition: G(A) := {(x,Ax) |x ∈ D} is called the graph of A. Obviously, G(A) is a linear subspace of X × Y . The linear operator A is called closed if G(A) is closed in X × Y . The ...

the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...